GAT General (NTS) chapter 6: Quantitative · Algebra MCQs with answers

By Team Megalecture · Updated 4 Nov 2026

56 exam-style questions on Quantitative · Algebra, each with the answer and a short explanation. Ten of them are below to try. The chapter test draws ten fresh questions each time and is marked the moment you finish, with your score by topic.

56 questions · 4 topics · 10 per test

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What chapter 6 covers

Ten Quantitative · Algebra questions with answers

Try each one, then open the answer. These ten stay the same; the test draws new ones every time.

1. Ayesha is three times as old as Bilal. In 8 years she will be twice as old as him. How old is Bilal now?

  1. A
    8 years
  2. B
    16 years
  3. C
    24 years
  4. D
    4 years
Show answer

Answer: A. Let Bilal be b, so Ayesha is 3b. Then 3b + 8 = 2(b + 8) gives b = 8. Ayesha is 24 now, which is the tempting wrong pick.

2. If (2x − 1)/3 = (x + 4)/2, then x =

  1. A
    10
  2. B
    14
  3. C
    2
  4. D
    7
Show answer

Answer: B. Cross-multiply: 2(2x − 1) = 3(x + 4), so 4x − 2 = 3x + 12 and x = 14. Check: both sides equal 9.

3. If x = √3 + √2, then x2 =

  1. A
    5
  2. B
    5 + √6
  3. C
    5 + 2√6
  4. D
    5 + 2√5
Show answer

Answer: C. (√3 + √2)2 = 3 + 2√3·√2 + 2 = 5 + 2√6. Leaving out the middle term gives 5.

4. The next number in the pattern 2, 6, 12, 20, 30, ... is

  1. A
    42
  2. B
    40
  3. C
    44
  4. D
    36
Show answer

Answer: A. The differences are 4, 6, 8, 10, so the next difference is 12 and the term is 42 (equivalently n(n + 1) with n = 6).

5. Which term of the arithmetic sequence 7, 10, 13, ... is 100?

  1. A
    31st
  2. B
    32nd
  3. C
    33rd
  4. D
    30th
Show answer

Answer: B. 7 + 3(n − 1) = 100 gives n − 1 = 31, so n = 32. Stopping at 31 forgets the +1.

6. The inverse of the matrix with rows [3 1] and [5 2] has rows

  1. A
    [2 −1] and [−5 3]
  2. B
    [3 −1] and [−5 2]
  3. C
    [−2 1] and [5 −3]
  4. D
    [2 5] and [1 3]
Show answer

Answer: A. The determinant is 6 − 5 = 1. Swap the diagonal entries and change the sign of the other two: rows [2 −1] and [−5 3]. Changing signs without swapping, or swapping without changing signs, gives a wrong matrix.

7. 1/(√5 − 2) with a rational denominator is

  1. A
    √5 − 2
  2. B
    √5 + 2
  3. C
    (√5 + 2)/3
  4. D
    (√5 − 2)/9
Show answer

Answer: B. Multiply top and bottom by √5 + 2: the denominator becomes (√5)2 − 22 = 5 − 4 = 1, so the value is √5 + 2.

8. The geometric mean of 4 and 25 is

  1. A
    14.5
  2. B
    100
  3. C
    29
  4. D
    10
Show answer

Answer: D. G = √(4 × 25) = √100 = 10. 14.5 is the arithmetic mean and 100 is the product itself.

9. If f(x) = 2x2 − 3x + 1, then f(−2) =

  1. A
    15
  2. B
    3
  3. C
    −1
  4. D
    11
Show answer

Answer: A. f(−2) = 2(4) − 3(−2) + 1 = 8 + 6 + 1 = 15. Taking −3(−2) as −6 gives 3.

10. The digits of a two-digit number add to 11. Reversing the digits makes the number larger by 27. The number is

  1. A
    74
  2. B
    38
  3. C
    56
  4. D
    47
Show answer

Answer: D. With tens digit t and units digit u: t + u = 11 and (10u + t) − (10t + u) = 9(u − t) = 27, so u − t = 3. Hence u = 7, t = 4 and the number is 47. 74 is the reversed number.

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Ways to practise this chapter

Quantitative · Algebra: questions students ask

How many Quantitative · Algebra MCQs are there?

56, each with the answer and a short explanation, across 4 topics: Linear equations and inequalities, Exponents, radicals and quadratics, Sequences and series, Matrices and basic functions. Every chapter test draws ten of them, so you can take it many times.

Is the GAT General (NTS) chapter 6 test free?

Yes. The test, the answers and the explanations are free and need no sign-up. Sign in only if you want your scores kept across devices.

How is the chapter test marked?

The moment you press Finish: your score, the right answer and an explanation for every question, and the ones you got wrong saved in My mistakes to retry.

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